LMFDB - Embedded newform 43.6.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-4.38824$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} +O(q^{10})$	\(q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} -2.46078 q^{10} -65.6764 q^{11} -74.3080 q^{12} -689.371 q^{13} +897.236 q^{14} -11.4385 q^{15} -920.259 q^{16} +737.385 q^{17} +2070.77 q^{18} -609.887 q^{19} +1.35494 q^{20} +4170.63 q^{21} -353.880 q^{22} +1312.45 q^{23} -4718.95 q^{24} -3124.79 q^{25} -3714.50 q^{26} +3539.34 q^{27} -494.030 q^{28} -8969.74 q^{29} -61.6333 q^{30} +5858.93 q^{31} +1070.53 q^{32} -1644.94 q^{33} +3973.21 q^{34} -76.0477 q^{35} -1140.19 q^{36} -55.9069 q^{37} -3286.22 q^{38} -17266.1 q^{39} +86.0458 q^{40} -10450.3 q^{41} +22472.4 q^{42} +1849.00 q^{43} +194.851 q^{44} -175.514 q^{45} +7071.82 q^{46} +1942.82 q^{47} -23049.0 q^{48} +10921.1 q^{49} -16837.1 q^{50} +18468.7 q^{51} +2045.25 q^{52} +30129.2 q^{53} +19070.8 q^{54} +29.9941 q^{55} -31373.5 q^{56} -15275.3 q^{57} -48331.2 q^{58} +52167.4 q^{59} +33.9361 q^{60} -14040.1 q^{61} +31569.4 q^{62} +63994.7 q^{63} +35216.6 q^{64} +314.832 q^{65} -8863.36 q^{66} +51437.7 q^{67} -2187.70 q^{68} +32872.0 q^{69} -409.764 q^{70} +11268.6 q^{71} -72408.2 q^{72} -61124.5 q^{73} -301.240 q^{74} -78264.2 q^{75} +1809.44 q^{76} -10936.3 q^{77} -93034.1 q^{78} +96018.3 q^{79} +420.278 q^{80} -4740.91 q^{81} -56308.8 q^{82} +30378.0 q^{83} -12373.6 q^{84} -336.760 q^{85} +9962.86 q^{86} -224658. q^{87} +12374.1 q^{88} -65040.4 q^{89} -945.710 q^{90} -114792. q^{91} -3893.84 q^{92} +146744. q^{93} +10468.4 q^{94} +278.532 q^{95} +26812.8 q^{96} +12067.6 q^{97} +58845.3 q^{98} -25240.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.38824	0.952516	0.476258	−	0.879306i	$-0.341993\pi$
$2$	5.38824	0.952516	0.476258	+	0.879306i	$0.341993\pi$
$3$	25.0462	1.60671	0.803357	−	0.595497i	$-0.203045\pi$
$3$	25.0462	1.60671	0.803357	+	0.595497i	$0.203045\pi$
$4$	−2.96684	−0.0927137
$5$	−0.456695	−0.00816961	−0.00408481	−	0.999992i	$-0.501300\pi$
$5$	−0.456695	−0.00816961	−0.00408481	+	0.999992i	$0.501300\pi$
$6$	134.955	1.53042
$7$	166.517	1.28444	0.642221	−	0.766519i	$-0.278013\pi$
$7$	166.517	1.28444	0.642221	+	0.766519i	$0.278013\pi$
$8$	−188.410	−1.04083
$9$	384.312	1.58153
$10$	−2.46078	−0.00778168
$11$	−65.6764	−0.163654	−0.0818272	−	0.996647i	$-0.526076\pi$
$11$	−65.6764	−0.163654	−0.0818272	+	0.996647i	$0.526076\pi$
$12$	−74.3080	−0.148964
$13$	−689.371	−1.13134	−0.565672	−	0.824630i	$-0.691383\pi$
$13$	−689.371	−1.13134	−0.565672	+	0.824630i	$0.691383\pi$
$14$	897.236	1.22345
$15$	−11.4385	−0.0131262
$16$	−920.259	−0.898690
$17$	737.385	0.618831	0.309415	−	0.950927i	$-0.399867\pi$
$17$	737.385	0.618831	0.309415	+	0.950927i	$0.399867\pi$
$18$	2070.77	1.50643
$19$	−609.887	−0.387583	−0.193792	−	0.981043i	$-0.562079\pi$
$19$	−609.887	−0.387583	−0.193792	+	0.981043i	$0.562079\pi$
$20$	1.35494	0.000757435 0
$21$	4170.63	2.06373
$22$	−353.880	−0.155883
$23$	1312.45	0.517326	0.258663	−	0.965968i	$-0.416718\pi$
$23$	1312.45	0.517326	0.258663	+	0.965968i	$0.416718\pi$
$24$	−4718.95	−1.67231
$25$	−3124.79	−0.999933
$26$	−3714.50	−1.07762
$27$	3539.34	0.934357
$28$	−494.030	−0.119085
$29$	−8969.74	−1.98055	−0.990273	−	0.139137i	$-0.955567\pi$
$29$	−8969.74	−1.98055	−0.990273	+	0.139137i	$0.955567\pi$
$30$	−61.6333	−0.0125029
$31$	5858.93	1.09500	0.547500	−	0.836806i	$-0.315580\pi$
$31$	5858.93	1.09500	0.547500	+	0.836806i	$0.315580\pi$
$32$	1070.53	0.184810
$33$	−1644.94	−0.262946
$34$	3973.21	0.589446
$35$	−76.0477	−0.0104934
$36$	−1140.19	−0.146630
$37$	−55.9069	−0.00671369	−0.00335685	−	0.999994i	$-0.501069\pi$
$37$	−55.9069	−0.00671369	−0.00335685	+	0.999994i	$0.501069\pi$
$38$	−3286.22	−0.369179
$39$	−17266.1	−1.81775
$40$	86.0458	0.00850315
$41$	−10450.3	−0.970889	−0.485445	−	0.874267i	$-0.661342\pi$
$41$	−10450.3	−0.970889	−0.485445	+	0.874267i	$0.661342\pi$
$42$	22472.4	1.96574
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	194.851	0.0151730
$45$	−175.514	−0.0129205
$46$	7071.82	0.492762
$47$	1942.82	0.128288	0.0641442	−	0.997941i	$-0.479568\pi$
$47$	1942.82	0.128288	0.0641442	+	0.997941i	$0.479568\pi$
$48$	−23049.0	−1.44394
$49$	10921.1	0.649792
$50$	−16837.1	−0.952452
$51$	18468.7	0.994284
$52$	2045.25	0.104891
$53$	30129.2	1.47332	0.736661	−	0.676262i	$-0.236401\pi$
$53$	30129.2	1.47332	0.736661	+	0.676262i	$0.236401\pi$
$54$	19070.8	0.889989
$55$	29.9941	0.00133699
$56$	−31373.5	−1.33688
$57$	−15275.3	−0.622736
$58$	−48331.2	−1.88650
$59$	52167.4	1.95106	0.975528	−	0.219877i	$-0.0705657\pi$
$59$	52167.4	1.95106	0.975528	+	0.219877i	$0.0705657\pi$
$60$	33.9361	0.00121698
$61$	−14040.1	−0.483108	−0.241554	−	0.970387i	$-0.577657\pi$
$61$	−14040.1	−0.483108	−0.241554	+	0.970387i	$0.577657\pi$
$62$	31569.4	1.04301
$63$	63994.7	2.03139
$64$	35216.6	1.07473
$65$	314.832	0.00924264
$66$	−8863.36	−0.250460
$67$	51437.7	1.39989	0.699946	−	0.714196i	$-0.253208\pi$
$67$	51437.7	1.39989	0.699946	+	0.714196i	$0.253208\pi$
$68$	−2187.70	−0.0573741
$69$	32872.0	0.831196
$70$	−409.764	−0.00999512
$71$	11268.6	0.265292	0.132646	−	0.991163i	$-0.457653\pi$
$71$	11268.6	0.265292	0.132646	+	0.991163i	$0.457653\pi$
$72$	−72408.2	−1.64610
$73$	−61124.5	−1.34248	−0.671241	−	0.741239i	$-0.734238\pi$
$73$	−61124.5	−1.34248	−0.671241	+	0.741239i	$0.734238\pi$
$74$	−301.240	−0.00639490
$75$	−78264.2	−1.60661
$76$	1809.44	0.0359343
$77$	−10936.3	−0.210205
$78$	−93034.1	−1.73143
$79$	96018.3	1.73096	0.865478	−	0.500947i	$-0.167015\pi$
$79$	96018.3	1.73096	0.865478	+	0.500947i	$0.167015\pi$
$80$	420.278	0.00734195
$81$	−4740.91	−0.0802878
$82$	−56308.8	−0.924787
$83$	30378.0	0.484021	0.242010	−	0.970274i	$-0.422193\pi$
$83$	30378.0	0.484021	0.242010	+	0.970274i	$0.422193\pi$
$84$	−12373.6	−0.191336
$85$	−336.760	−0.00505561
$86$	9962.86	0.145257
$87$	−224658.	−3.18217
$88$	12374.1	0.170336
$89$	−65040.4	−0.870378	−0.435189	−	0.900339i	$-0.643319\pi$
$89$	−65040.4	−0.870378	−0.435189	+	0.900339i	$0.643319\pi$
$90$	−945.710	−0.0123070
$91$	−114792.	−1.45315
$92$	−3893.84	−0.0479632
$93$	146744.	1.75935
$94$	10468.4	0.122197
$95$	278.532	0.00316641
$96$	26812.8	0.296937
$97$	12067.6	0.130224	0.0651119	−	0.997878i	$-0.479260\pi$
$97$	12067.6	0.130224	0.0651119	+	0.997878i	$0.479260\pi$
$98$	58845.3	0.618938
$99$	−25240.2	−0.258825
$100$	9270.75	0.0927075
$101$	107046.	1.04416	0.522079	−	0.852897i	$-0.325157\pi$
$101$	107046.	1.04416	0.522079	+	0.852897i	$0.325157\pi$
$102$	99513.8	0.947072
$103$	−86209.7	−0.800688	−0.400344	−	0.916365i	$-0.631109\pi$
$103$	−86209.7	−0.800688	−0.400344	+	0.916365i	$0.631109\pi$
$104$	129884.	1.17753
$105$	−1904.71	−0.0168599
$106$	162343.	1.40336
$107$	197153.	1.66473	0.832365	−	0.554227i	$-0.186986\pi$
$107$	197153.	1.66473	0.832365	+	0.554227i	$0.186986\pi$
$108$	−10500.6	−0.0866276
$109$	165311.	1.33271	0.666355	−	0.745634i	$-0.267853\pi$
$109$	165311.	1.33271	0.666355	+	0.745634i	$0.267853\pi$
$110$	161.615	0.00127351
$111$	−1400.26	−0.0107870
$112$	−153239.	−1.15432
$113$	−179790.	−1.32455	−0.662275	−	0.749260i	$-0.730409\pi$
$113$	−179790.	−1.32455	−0.662275	+	0.749260i	$0.730409\pi$
$114$	−82307.3	−0.593166
$115$	−599.391	−0.00422635
$116$	26611.8	0.183624
$117$	−264934.	−1.78926
$118$	281091.	1.85841
$119$	122787.	0.794852
$120$	2155.12	0.0136621
$121$	−156738.	−0.973217
$122$	−75651.3	−0.460168
$123$	−261741.	−1.55994
$124$	−17382.5	−0.101522
$125$	2854.25	0.0163387
$126$	344819.	1.93493
$127$	−286585.	−1.57668	−0.788341	−	0.615238i	$-0.789060\pi$
$127$	−286585.	−1.57668	−0.788341	+	0.615238i	$0.789060\pi$
$128$	155498.	0.838882
$129$	46310.4	0.245022
$130$	1696.39	0.00880376
$131$	67619.1	0.344263	0.172132	−	0.985074i	$-0.444935\pi$
$131$	67619.1	0.344263	0.172132	+	0.985074i	$0.444935\pi$
$132$	4880.28	0.0243787
$133$	−101557.	−0.497829
$134$	277159.	1.33342
$135$	−1616.40	−0.00763333
$136$	−138931.	−0.644096
$137$	133580.	0.608050	0.304025	−	0.952664i	$-0.401669\pi$
$137$	133580.	0.608050	0.304025	+	0.952664i	$0.401669\pi$
$138$	177122.	0.791727
$139$	−262195.	−1.15103	−0.575516	−	0.817790i	$-0.695199\pi$
$139$	−262195.	−1.15103	−0.575516	+	0.817790i	$0.695199\pi$
$140$	225.621	0.000972881 0
$141$	48660.2	0.206123
$142$	60718.0	0.252695
$143$	45275.4	0.185149
$144$	−353667.	−1.42131
$145$	4096.44	0.0161803
$146$	−329354.	−1.27873
$147$	273531.	1.04403
$148$	165.867	0.000622451 0
$149$	187414.	0.691569	0.345785	−	0.938314i	$-0.387613\pi$
$149$	187414.	0.691569	0.345785	+	0.938314i	$0.387613\pi$
$150$	−421706.	−1.53032
$151$	−131632.	−0.469807	−0.234904	−	0.972019i	$-0.575477\pi$
$151$	−131632.	−0.469807	−0.234904	+	0.972019i	$0.575477\pi$
$152$	114909.	0.403407
$153$	283386.	0.978701
$154$	−58927.3	−0.200223
$155$	−2675.75	−0.00894573
$156$	51225.8	0.168530
$157$	−252270.	−0.816800	−0.408400	−	0.912803i	$-0.633913\pi$
$157$	−252270.	−0.816800	−0.408400	+	0.912803i	$0.633913\pi$
$158$	517370.	1.64876
$159$	754622.	2.36721
$160$	−488.908	−0.00150983
$161$	218547.	0.664476
$162$	−25545.2	−0.0764754
$163$	−518121.	−1.52743	−0.763717	−	0.645552i	$-0.776627\pi$
$163$	−518121.	−1.52743	−0.763717	+	0.645552i	$0.776627\pi$
$164$	31004.4	0.0900147
$165$	751.238	0.00214817
$166$	163684.	0.461038
$167$	−681328.	−1.89045	−0.945224	−	0.326422i	$-0.894157\pi$
$167$	−681328.	−1.89045	−0.945224	+	0.326422i	$0.894157\pi$
$168$	−785788.	−2.14799
$169$	103939.	0.279939
$170$	−1814.54	−0.00481554
$171$	−234387.	−0.612976
$172$	−5485.68	−0.0141387
$173$	−148596.	−0.377478	−0.188739	−	0.982027i	$-0.560440\pi$
$173$	−148596.	−0.377478	−0.188739	+	0.982027i	$0.560440\pi$
$174$	−1.21051e6	−3.03107
$175$	−520332.	−1.28436
$176$	60439.3	0.147075
$177$	1.30660e6	3.13479
$178$	−350453.	−0.829049
$179$	103068.	0.240432	0.120216	−	0.992748i	$-0.461641\pi$
$179$	103068.	0.240432	0.120216	+	0.992748i	$0.461641\pi$
$180$	520.720	0.00119791
$181$	309316.	0.701789	0.350894	−	0.936415i	$-0.385878\pi$
$181$	309316.	0.701789	0.350894	+	0.936415i	$0.385878\pi$
$182$	−618529.	−1.38414
$183$	−351650.	−0.776217
$184$	−247279.	−0.538447
$185$	25.5324	5.48483e−5 0
$186$	790693.	1.67581
$187$	−48428.8	−0.101274
$188$	−5764.02	−0.0118941
$189$	589362.	1.20013
$190$	1500.80	0.00301605
$191$	373258.	0.740330	0.370165	−	0.928966i	$-0.379301\pi$
$191$	373258.	0.740330	0.370165	+	0.928966i	$0.379301\pi$
$192$	882042.	1.72678
$193$	85782.8	0.165770	0.0828852	−	0.996559i	$-0.473587\pi$
$193$	85782.8	0.165770	0.0828852	+	0.996559i	$0.473587\pi$
$194$	65023.0	0.124040
$195$	7885.36	0.0148503
$196$	−32401.0	−0.0602446
$197$	−178146.	−0.327047	−0.163523	−	0.986539i	$-0.552286\pi$
$197$	−178146.	−0.327047	−0.163523	+	0.986539i	$0.552286\pi$
$198$	−136001.	−0.246535
$199$	154725.	0.276967	0.138484	−	0.990365i	$-0.455777\pi$
$199$	154725.	0.276967	0.138484	+	0.990365i	$0.455777\pi$
$200$	588741.	1.04076
$201$	1.28832e6	2.24923
$202$	576789.	0.994577
$203$	−1.49362e6	−2.54390
$204$	−54793.6	−0.0921838
$205$	4772.61	0.00793179
$206$	−464519.	−0.762668
$207$	504392.	0.818168
$208$	634400.	1.01673
$209$	40055.2	0.0634297
$210$	−10263.0	−0.0160593
$211$	−682180.	−1.05485	−0.527427	−	0.849600i	$-0.676843\pi$
$211$	−682180.	−1.05485	−0.527427	+	0.849600i	$0.676843\pi$
$212$	−89388.4	−0.136597
$213$	282236.	0.426249
$214$	1.06231e6	1.58568
$215$	−844.429	−0.00124585
$216$	−666846.	−0.972504
$217$	975615.	1.40647
$218$	890736.	1.26943
$219$	−1.53094e6	−2.15698
$220$	−88.9876	−0.000123957 0
$221$	−508332.	−0.700110
$222$	−7544.92	−0.0102748
$223$	−464004.	−0.624827	−0.312413	−	0.949946i	$-0.601137\pi$
$223$	−464004.	−0.624827	−0.312413	+	0.949946i	$0.601137\pi$
$224$	178263.	0.237378
$225$	−1.20090e6	−1.58143
$226$	−968750.	−1.26166
$227$	1.13876e6	1.46679	0.733396	−	0.679801i	$-0.237934\pi$
$227$	1.13876e6	1.46679	0.733396	+	0.679801i	$0.237934\pi$
$228$	45319.5	0.0577361
$229$	648718.	0.817462	0.408731	−	0.912655i	$-0.365971\pi$
$229$	648718.	0.817462	0.408731	+	0.912655i	$0.365971\pi$
$230$	−3229.67	−0.00402567
$231$	−273912.	−0.337739
$232$	1.68999e6	2.06141
$233$	−588684.	−0.710383	−0.355191	−	0.934794i	$-0.615584\pi$
$233$	−588684.	−0.710383	−0.355191	+	0.934794i	$0.615584\pi$
$234$	−1.42753e6	−1.70430
$235$	−887.275	−0.00104807
$236$	−154772.	−0.180889
$237$	2.40489e6	2.78115
$238$	661608.	0.757109
$239$	739129.	0.837000	0.418500	−	0.908217i	$-0.362556\pi$
$239$	739129.	0.837000	0.418500	+	0.908217i	$0.362556\pi$
$240$	10526.4	0.0117964
$241$	−1.57360e6	−1.74523	−0.872615	−	0.488409i	$-0.837577\pi$
$241$	−1.57360e6	−1.74523	−0.872615	+	0.488409i	$0.837577\pi$
$242$	−844540.	−0.927005
$243$	−978801.	−1.06336
$244$	41654.6	0.0447908
$245$	−4987.60	−0.00530855
$246$	−1.41032e6	−1.48587
$247$	420438.	0.438490
$248$	−1.10388e6	−1.13971
$249$	760854.	0.777684
$250$	15379.4	0.0155628
$251$	456789.	0.457648	0.228824	−	0.973468i	$-0.426512\pi$
$251$	456789.	0.457648	0.228824	+	0.973468i	$0.426512\pi$
$252$	−189862.	−0.188337
$253$	−86197.3	−0.0846627
$254$	−1.54419e6	−1.50181
$255$	−8434.56	−0.00812292
$256$	−289068.	−0.275676
$257$	1.12132e6	1.05900	0.529499	−	0.848310i	$-0.322380\pi$
$257$	1.12132e6	1.05900	0.529499	+	0.848310i	$0.322380\pi$
$258$	249532.	0.233387
$259$	−9309.48	−0.00862335
$260$	−934.057	−0.000856919 0
$261$	−3.44718e6	−3.13230
$262$	364348.	0.327916
$263$	1.75620e6	1.56562	0.782808	−	0.622263i	$-0.213786\pi$
$263$	1.75620e6	1.56562	0.782808	+	0.622263i	$0.213786\pi$
$264$	309924.	0.273681
$265$	−13759.9	−0.0120365
$266$	−547213.	−0.474190
$267$	−1.62901e6	−1.39845
$268$	−152607.	−0.129789
$269$	1.22933e6	1.03583	0.517915	−	0.855432i	$-0.326708\pi$
$269$	1.22933e6	1.03583	0.517915	+	0.855432i	$0.326708\pi$
$270$	−8709.55	−0.00727087
$271$	1.32305e6	1.09435	0.547173	−	0.837020i	$-0.315704\pi$
$271$	1.32305e6	1.09435	0.547173	+	0.837020i	$0.315704\pi$
$272$	−678585.	−0.556137
$273$	−2.87511e6	−2.33479
$274$	719760.	0.579177
$275$	205225.	0.163643
$276$	−97525.9	−0.0770632
$277$	1.96854e6	1.54151	0.770754	−	0.637133i	$-0.219880\pi$
$277$	1.96854e6	1.54151	0.770754	+	0.637133i	$0.219880\pi$
$278$	−1.41277e6	−1.09638
$279$	2.25166e6	1.73178
$280$	14328.1	0.0109218
$281$	−1.11820e6	−0.844801	−0.422400	−	0.906409i	$-0.638812\pi$
$281$	−1.11820e6	−0.844801	−0.422400	+	0.906409i	$0.638812\pi$
$282$	262193.	0.196335
$283$	1.25727e6	0.933174	0.466587	−	0.884475i	$-0.345483\pi$
$283$	1.25727e6	0.933174	0.466587	+	0.884475i	$0.345483\pi$
$284$	−33432.2	−0.0245962
$285$	6976.18	0.00508751
$286$	243955.	0.176358
$287$	−1.74016e6	−1.24705
$288$	411420.	0.292283
$289$	−876121.	−0.617049
$290$	22072.6	0.0154120
$291$	302247.	0.209233
$292$	181347.	0.124466
$293$	−260406.	−0.177207	−0.0886037	−	0.996067i	$-0.528240\pi$
$293$	−260406.	−0.177207	−0.0886037	+	0.996067i	$0.528240\pi$
$294$	1.47385e6	0.994456
$295$	−23824.6	−0.0159394
$296$	10533.4	0.00698779
$297$	−232451.	−0.152912
$298$	1.00983e6	0.658731
$299$	−904768.	−0.585274
$300$	232197.	0.148954
$301$	307891.	0.195876
$302$	−709266.	−0.447499
$303$	2.68109e6	1.67766
$304$	561254.	0.348318
$305$	6412.03	0.00394681
$306$	1.52695e6	0.932228
$307$	−1.56144e6	−0.945536	−0.472768	−	0.881187i	$-0.656745\pi$
$307$	−1.56144e6	−0.945536	−0.472768	+	0.881187i	$0.656745\pi$
$308$	32446.1	0.0194888
$309$	−2.15923e6	−1.28648
$310$	−14417.6	−0.00852095
$311$	655137.	0.384088	0.192044	−	0.981386i	$-0.438488\pi$
$311$	655137.	0.384088	0.192044	+	0.981386i	$0.438488\pi$
$312$	3.25311e6	1.89196
$313$	−212890.	−0.122827	−0.0614136	−	0.998112i	$-0.519561\pi$
$313$	−212890.	−0.122827	−0.0614136	+	0.998112i	$0.519561\pi$
$314$	−1.35929e6	−0.778015
$315$	−29226.1	−0.0165956
$316$	−284871.	−0.160483
$317$	−385858.	−0.215665	−0.107832	−	0.994169i	$-0.534391\pi$
$317$	−385858.	−0.215665	−0.107832	+	0.994169i	$0.534391\pi$
$318$	4.06608e6	2.25480
$319$	589100.	0.324125
$320$	−16083.2	−0.00878009
$321$	4.93794e6	2.67475
$322$	1.17758e6	0.632924
$323$	−449721.	−0.239849
$324$	14065.5	0.00744378
$325$	2.15414e6	1.13127
$326$	−2.79176e6	−1.45490
$327$	4.14042e6	2.14129
$328$	1.96894e6	1.01053
$329$	323513.	0.164779
$330$	4047.85	0.00204616
$331$	−1.62905e6	−0.817269	−0.408634	−	0.912698i	$-0.633995\pi$
$331$	−1.62905e6	−0.817269	−0.408634	+	0.912698i	$0.633995\pi$
$332$	−90126.6	−0.0448754
$333$	−21485.7	−0.0106179
$334$	−3.67116e6	−1.80068
$335$	−23491.3	−0.0114366
$336$	−3.83806e6	−1.85466
$337$	−2.32344e6	−1.11444	−0.557220	−	0.830365i	$-0.688132\pi$
$337$	−2.32344e6	−1.11444	−0.557220	+	0.830365i	$0.688132\pi$
$338$	560050.	0.266646
$339$	−4.50305e6	−2.12818
$340$	999.112	0.000468724 0
$341$	−384794.	−0.179202
$342$	−1.26293e6	−0.583869
$343$	−980112.	−0.449822
$344$	−348370.	−0.158725
$345$	−15012.5	−0.00679055
$346$	−800670.	−0.359553
$347$	−2.45789e6	−1.09582	−0.547910	−	0.836537i	$-0.684576\pi$
$347$	−2.45789e6	−1.09582	−0.547910	+	0.836537i	$0.684576\pi$
$348$	666524.	0.295031
$349$	−4.36489e6	−1.91827	−0.959135	−	0.282950i	$-0.908687\pi$
$349$	−4.36489e6	−1.91827	−0.959135	+	0.282950i	$0.908687\pi$
$350$	−2.80368e6	−1.22337
$351$	−2.43992e6	−1.05708
$352$	−70308.9	−0.0302450
$353$	898354.	0.383717	0.191858	−	0.981423i	$-0.438549\pi$
$353$	898354.	0.383717	0.191858	+	0.981423i	$0.438549\pi$
$354$	7.04026e6	2.98594
$355$	−5146.32	−0.00216734
$356$	192964.	0.0806960
$357$	3.07536e6	1.27710
$358$	555357.	0.229015
$359$	1.81866e6	0.744759	0.372379	−	0.928081i	$-0.378542\pi$
$359$	1.81866e6	0.744759	0.372379	+	0.928081i	$0.378542\pi$
$360$	33068.5	0.0134480
$361$	−2.10414e6	−0.849779
$362$	1.66667e6	0.668465
$363$	−3.92568e6	−1.56368
$364$	340570.	0.134727
$365$	27915.3	0.0109675
$366$	−1.89478e6	−0.739359
$367$	−2.34762e6	−0.909836	−0.454918	−	0.890533i	$-0.650331\pi$
$367$	−2.34762e6	−0.909836	−0.454918	+	0.890533i	$0.650331\pi$
$368$	−1.20780e6	−0.464916
$369$	−4.01619e6	−1.53549
$370$	137.575	5.22438e−5 0
$371$	5.01703e6	1.89240
$372$	−435366.	−0.163116
$373$	2.97881e6	1.10859	0.554295	−	0.832321i	$-0.312988\pi$
$373$	2.97881e6	1.10859	0.554295	+	0.832321i	$0.312988\pi$
$374$	−260946.	−0.0964654
$375$	71488.1	0.0262516
$376$	−366046.	−0.133526
$377$	6.18348e6	2.24068
$378$	3.17562e6	1.14314
$379$	1.77718e6	0.635527	0.317764	−	0.948170i	$-0.397068\pi$
$379$	1.77718e6	0.635527	0.317764	+	0.948170i	$0.397068\pi$
$380$	−826.360	−0.000293569 0
$381$	−7.17787e6	−2.53328
$382$	2.01120e6	0.705176
$383$	−2.08193e6	−0.725220	−0.362610	−	0.931941i	$-0.618114\pi$
$383$	−2.08193e6	−0.725220	−0.362610	+	0.931941i	$0.618114\pi$
$384$	3.89465e6	1.34784
$385$	4994.54	0.00171729
$386$	462219.	0.157899
$387$	710594.	0.241181
$388$	−35802.5	−0.0120735
$389$	−1.81080e6	−0.606730	−0.303365	−	0.952874i	$-0.598110\pi$
$389$	−1.81080e6	−0.606730	−0.303365	+	0.952874i	$0.598110\pi$
$390$	42488.2	0.0141451
$391$	967784.	0.320137
$392$	−2.05764e6	−0.676321
$393$	1.69360e6	0.553133
$394$	−959892.	−0.311517
$395$	−43851.1	−0.0141412
$396$	74883.7	0.0239966
$397$	185900.	0.0591975	0.0295988	−	0.999562i	$-0.490577\pi$
$397$	185900.	0.0591975	0.0295988	+	0.999562i	$0.490577\pi$
$398$	833697.	0.263816
$399$	−2.54361e6	−0.799869
$400$	2.87562e6	0.898631
$401$	−3.41892e6	−1.06176	−0.530882	−	0.847446i	$-0.678139\pi$
$401$	−3.41892e6	−1.06176	−0.530882	+	0.847446i	$0.678139\pi$
$402$	6.94177e6	2.14242
$403$	−4.03898e6	−1.23882
$404$	−317587.	−0.0968077
$405$	2165.15	0.000655920 0
$406$	−8.04798e6	−2.42310
$407$	3671.77	0.00109873
$408$	−3.47968e6	−1.03488
$409$	−428179.	−0.126566	−0.0632830	−	0.997996i	$-0.520157\pi$
$409$	−428179.	−0.126566	−0.0632830	+	0.997996i	$0.520157\pi$
$410$	25716.0	0.00755515
$411$	3.34567e6	0.976963
$412$	255770.	0.0742347
$413$	8.68679e6	2.50602
$414$	2.71779e6	0.779318
$415$	−13873.5	−0.00395426
$416$	−737996.	−0.209084
$417$	−6.56699e6	−1.84938
$418$	215827.	0.0604178
$419$	3.84011e6	1.06858	0.534292	−	0.845300i	$-0.320578\pi$
$419$	3.84011e6	1.06858	0.534292	+	0.845300i	$0.320578\pi$
$420$	5650.95	0.00156314
$421$	7.05884e6	1.94101	0.970506	−	0.241078i	$-0.0775010\pi$
$421$	7.05884e6	1.94101	0.970506	+	0.241078i	$0.0775010\pi$
$422$	−3.67575e6	−1.00477
$423$	746649.	0.202892
$424$	−5.67663e6	−1.53347
$425$	−2.30417e6	−0.618789
$426$	1.52076e6	0.406009
$427$	−2.33792e6	−0.620525
$428$	−584921.	−0.154343
$429$	1.13398e6	0.297482
$430$	−4549.99	−0.00118670
$431$	−2.11813e6	−0.549237	−0.274619	−	0.961553i	$-0.588552\pi$
$431$	−2.11813e6	−0.549237	−0.274619	+	0.961553i	$0.588552\pi$
$432$	−3.25711e6	−0.839697
$433$	−1.58858e6	−0.407182	−0.203591	−	0.979056i	$-0.565261\pi$
$433$	−1.58858e6	−0.407182	−0.203591	+	0.979056i	$0.565261\pi$
$434$	5.25685e6	1.33968
$435$	102600.	0.0259971
$436$	−490451.	−0.123560
$437$	−800448.	−0.200507
$438$	−8.24906e6	−2.05456
$439$	7.11302e6	1.76154	0.880771	−	0.473543i	$-0.157025\pi$
$439$	7.11302e6	1.76154	0.880771	+	0.473543i	$0.157025\pi$
$440$	−5651.18	−0.00139158
$441$	4.19710e6	1.02767
$442$	−2.73901e6	−0.666866
$443$	2.52423e6	0.611110	0.305555	−	0.952174i	$-0.401158\pi$
$443$	2.52423e6	0.611110	0.305555	+	0.952174i	$0.401158\pi$
$444$	4154.33	0.00100010
$445$	29703.6	0.00711065
$446$	−2.50017e6	−0.595157
$447$	4.69400e6	1.11115
$448$	5.86418e6	1.38042
$449$	−471868.	−0.110460	−0.0552300	−	0.998474i	$-0.517589\pi$
$449$	−471868.	−0.110460	−0.0552300	+	0.998474i	$0.517589\pi$
$450$	−6.47072e6	−1.50633
$451$	686339.	0.158890
$452$	533407.	0.122804
$453$	−3.29689e6	−0.754846
$454$	6.13593e6	1.39714
$455$	52425.1	0.0118716
$456$	2.87803e6	0.648160
$457$	−6.11039e6	−1.36861	−0.684303	−	0.729198i	$-0.739893\pi$
$457$	−6.11039e6	−1.36861	−0.684303	+	0.729198i	$0.739893\pi$
$458$	3.49545e6	0.778645
$459$	2.60985e6	0.578209
$460$	1778.30	0.000391841 0
$461$	7.47383e6	1.63791	0.818957	−	0.573855i	$-0.194553\pi$
$461$	7.47383e6	1.63791	0.818957	+	0.573855i	$0.194553\pi$
$462$	−1.47590e6	−0.321702
$463$	−4.14981e6	−0.899654	−0.449827	−	0.893116i	$-0.648514\pi$
$463$	−4.14981e6	−0.899654	−0.449827	+	0.893116i	$0.648514\pi$
$464$	8.25449e6	1.77990
$465$	−67017.3	−0.0143732
$466$	−3.17197e6	−0.676651
$467$	−1.18789e6	−0.252048	−0.126024	−	0.992027i	$-0.540222\pi$
$467$	−1.18789e6	−0.252048	−0.126024	+	0.992027i	$0.540222\pi$
$468$	786016.	0.165889
$469$	8.56527e6	1.79808
$470$	−4780.86	−0.000998300 0
$471$	−6.31840e6	−1.31237
$472$	−9.82886e6	−2.03071
$473$	−121436.	−0.0249571
$474$	1.29581e7	2.64909
$475$	1.90577e6	0.387558
$476$	−364290.	−0.0736937
$477$	1.15790e7	2.33011
$478$	3.98260e6	0.797255
$479$	3.74102e6	0.744992	0.372496	−	0.928034i	$-0.378502\pi$
$479$	3.74102e6	0.744992	0.372496	+	0.928034i	$0.378502\pi$
$480$	−12245.3	−0.00242586
$481$	38540.6	0.00759549
$482$	−8.47896e6	−1.66236
$483$	5.47376e6	1.06762
$484$	465015.	0.0902306
$485$	−5511.20	−0.00106388
$486$	−5.27402e6	−1.01286
$487$	7.18109e6	1.37204	0.686021	−	0.727581i	$-0.259356\pi$
$487$	7.18109e6	1.37204	0.686021	+	0.727581i	$0.259356\pi$
$488$	2.64529e6	0.502832
$489$	−1.29770e7	−2.45415
$490$	−26874.4	−0.00505648
$491$	−7.37443e6	−1.38046	−0.690231	−	0.723589i	$-0.742491\pi$
$491$	−7.37443e6	−1.38046	−0.690231	+	0.723589i	$0.742491\pi$
$492$	776542.	0.144628
$493$	−6.61415e6	−1.22562
$494$	2.26542e6	0.417669
$495$	11527.1	0.00211450
$496$	−5.39174e6	−0.984067
$497$	1.87642e6	0.340753
$498$	4.09967e6	0.740756
$499$	2.61086e6	0.469388	0.234694	−	0.972069i	$-0.424591\pi$
$499$	2.61086e6	0.469388	0.234694	+	0.972069i	$0.424591\pi$
$500$	−8468.09	−0.00151482
$501$	−1.70647e7	−3.03741
$502$	2.46129e6	0.435917
$503$	−398438.	−0.0702167	−0.0351084	−	0.999384i	$-0.511178\pi$
$503$	−398438.	−0.0702167	−0.0351084	+	0.999384i	$0.511178\pi$
$504$	−1.20572e7	−2.11432
$505$	−48887.3	−0.00853036
$506$	−464452.	−0.0806426
$507$	2.60329e6	0.449782
$508$	850251.	0.146180
$509$	556201.	0.0951563	0.0475781	−	0.998868i	$-0.484850\pi$
$509$	556201.	0.0951563	0.0475781	+	0.998868i	$0.484850\pi$
$510$	−45447.5	−0.00773721
$511$	−1.01783e7	−1.72434
$512$	−6.53352e6	−1.10147
$513$	−2.15860e6	−0.362141
$514$	6.04193e6	1.00871
$515$	39371.6	0.00654131
$516$	−137396.	−0.0227169
$517$	−127597.	−0.0209950
$518$	−50161.8	−0.00821388
$519$	−3.72176e6	−0.606499
$520$	−59317.5	−0.00961999
$521$	3.39465e6	0.547898	0.273949	−	0.961744i	$-0.411670\pi$
$521$	3.39465e6	0.547898	0.273949	+	0.961744i	$0.411670\pi$
$522$	−1.85743e7	−2.98356
$523$	−9.40326e6	−1.50323	−0.751613	−	0.659605i	$-0.770724\pi$
$523$	−9.40326e6	−1.50323	−0.751613	+	0.659605i	$0.770724\pi$
$524$	−200615.	−0.0319179
$525$	−1.30323e7	−2.06359
$526$	9.46285e6	1.49127
$527$	4.32029e6	0.677620
$528$	1.51377e6	0.236307
$529$	−4.71381e6	−0.732373
$530$	−74141.4	−0.0114649
$531$	2.00486e7	3.08566
$532$	301303.	0.0461555
$533$	7.20414e6	1.09841
$534$	−8.77753e6	−1.33205
$535$	−90038.8	−0.0136002
$536$	−9.69136e6	−1.45704
$537$	2.58147e6	0.386306
$538$	6.62393e6	0.986644
$539$	−717256.	−0.106341
$540$	4795.59	0.000707714 0
$541$	4.76159e6	0.699453	0.349727	−	0.936852i	$-0.386274\pi$
$541$	4.76159e6	0.699453	0.349727	+	0.936852i	$0.386274\pi$
$542$	7.12894e6	1.04238
$543$	7.74720e6	1.12757
$544$	789396.	0.114366
$545$	−75496.8	−0.0108877
$546$	−1.54918e7	−2.22393
$547$	4.68380e6	0.669314	0.334657	−	0.942340i	$-0.391379\pi$
$547$	4.68380e6	0.669314	0.334657	+	0.942340i	$0.391379\pi$
$548$	−396309.	−0.0563745
$549$	−5.39577e6	−0.764051
$550$	1.10580e6	0.155873
$551$	5.47053e6	0.767627
$552$	−6.19341e6	−0.865131
$553$	1.59887e7	2.22331
$554$	1.06070e7	1.46831
$555$	639.490	8.81255e−5 0
$556$	777890.	0.106716
$557$	4.37082e6	0.596931	0.298466	−	0.954420i	$-0.403525\pi$
$557$	4.37082e6	0.596931	0.298466	+	0.954420i	$0.403525\pi$
$558$	1.21325e7	1.64955
$559$	−1.27465e6	−0.172528
$560$	69983.6	0.00943031
$561$	−1.21296e6	−0.162719
$562$	−6.02514e6	−0.804686
$563$	−9.98439e6	−1.32755	−0.663774	−	0.747933i	$-0.731046\pi$
$563$	−9.98439e6	−1.32755	−0.663774	+	0.747933i	$0.731046\pi$
$564$	−144367.	−0.0191104
$565$	82109.1	0.0108211
$566$	6.77448e6	0.888863
$567$	−789445.	−0.103125
$568$	−2.12312e6	−0.276123
$569$	−3.03616e6	−0.393137	−0.196568	−	0.980490i	$-0.562980\pi$
$569$	−3.03616e6	−0.393137	−0.196568	+	0.980490i	$0.562980\pi$
$570$	37589.3	0.00484593
$571$	−4.66426e6	−0.598677	−0.299339	−	0.954147i	$-0.596766\pi$
$571$	−4.66426e6	−0.598677	−0.299339	+	0.954147i	$0.596766\pi$
$572$	−134325.	−0.0171659
$573$	9.34869e6	1.18950
$574$	−9.37640e6	−1.18784
$575$	−4.10115e6	−0.517292
$576$	1.35342e7	1.69971
$577$	2.53940e6	0.317536	0.158768	−	0.987316i	$-0.449248\pi$
$577$	2.53940e6	0.317536	0.158768	+	0.987316i	$0.449248\pi$
$578$	−4.72075e6	−0.587749
$579$	2.14853e6	0.266346
$580$	−12153.5	−0.00150013
$581$	5.05847e6	0.621697
$582$	1.62858e6	0.199297
$583$	−1.97878e6	−0.241116
$584$	1.15165e7	1.39729
$585$	120994.	0.0146175
$586$	−1.40313e6	−0.168793
$587$	1.18921e7	1.42450	0.712248	−	0.701927i	$-0.247677\pi$
$587$	1.18921e7	1.42450	0.712248	+	0.701927i	$0.247677\pi$
$588$	−811522.	−0.0967960
$589$	−3.57329e6	−0.424404
$590$	−128373.	−0.0151825
$591$	−4.46187e6	−0.525471
$592$	51448.9	0.00603353
$593$	1.49053e6	0.174062	0.0870311	−	0.996206i	$-0.472262\pi$
$593$	1.49053e6	0.174062	0.0870311	+	0.996206i	$0.472262\pi$
$594$	−1.25250e6	−0.145651
$595$	−56076.4	−0.00649363
$596$	−556026.	−0.0641179
$597$	3.87528e6	0.445008
$598$	−4.87511e6	−0.557483
$599$	−1.13339e7	−1.29066	−0.645328	−	0.763905i	$-0.723279\pi$
$599$	−1.13339e7	−1.29066	−0.645328	+	0.763905i	$0.723279\pi$
$600$	1.47457e7	1.67220
$601$	1.07157e7	1.21014	0.605069	−	0.796173i	$-0.293145\pi$
$601$	1.07157e7	1.21014	0.605069	+	0.796173i	$0.293145\pi$
$602$	1.65899e6	0.186575
$603$	1.97681e7	2.21397
$604$	390531.	0.0435576
$605$	71581.3	0.00795081
$606$	1.44464e7	1.59800
$607$	−871321.	−0.0959857	−0.0479929	−	0.998848i	$-0.515282\pi$
$607$	−871321.	−0.0959857	−0.0479929	+	0.998848i	$0.515282\pi$
$608$	−652905.	−0.0716293
$609$	−3.74095e7	−4.08732
$610$	34549.6	0.00375940
$611$	−1.33932e6	−0.145138
$612$	−840760.	−0.0907389
$613$	−1.62264e7	−1.74410	−0.872051	−	0.489415i	$-0.837210\pi$
$613$	−1.62264e7	−1.74410	−0.872051	+	0.489415i	$0.837210\pi$
$614$	−8.41339e6	−0.900638
$615$	119536.	0.0127441
$616$	2.06050e6	0.218787
$617$	1.18192e6	0.124990	0.0624950	−	0.998045i	$-0.480094\pi$
$617$	1.18192e6	0.124990	0.0624950	+	0.998045i	$0.480094\pi$
$618$	−1.16344e7	−1.22539
$619$	1.78346e7	1.87084	0.935418	−	0.353544i	$-0.115023\pi$
$619$	1.78346e7	1.87084	0.935418	+	0.353544i	$0.115023\pi$
$620$	7938.50	0.000829391 0
$621$	4.64522e6	0.483367
$622$	3.53004e6	0.365850
$623$	−1.08304e7	−1.11795
$624$	1.58893e7	1.63359
$625$	9.76367e6	0.999800
$626$	−1.14710e6	−0.116995
$627$	1.00323e6	0.101913
$628$	748443.	0.0757286
$629$	−41224.9	−0.00415464
$630$	−157477.	−0.0158076
$631$	−1.56569e7	−1.56543	−0.782715	−	0.622381i	$-0.786166\pi$
$631$	−1.56569e7	−1.56543	−0.782715	+	0.622381i	$0.786166\pi$
$632$	−1.80908e7	−1.80163
$633$	−1.70860e7	−1.69485
$634$	−2.07910e6	−0.205424
$635$	130882.	0.0128809
$636$	−2.23884e6	−0.219473
$637$	−7.52866e6	−0.735139
$638$	3.17422e6	0.308734
$639$	4.33067e6	0.419568
$640$	−71015.4	−0.00685334
$641$	−9.56677e6	−0.919645	−0.459822	−	0.888011i	$-0.652087\pi$
$641$	−9.56677e6	−0.919645	−0.459822	+	0.888011i	$0.652087\pi$
$642$	2.66068e7	2.54774
$643$	6.58449e6	0.628050	0.314025	−	0.949415i	$-0.398322\pi$
$643$	6.58449e6	0.628050	0.314025	+	0.949415i	$0.398322\pi$
$644$	−648392.	−0.0616060
$645$	−21149.7	−0.00200173
$646$	−2.42321e6	−0.228459
$647$	−5.77942e6	−0.542779	−0.271390	−	0.962470i	$-0.587483\pi$
$647$	−5.77942e6	−0.542779	−0.271390	+	0.962470i	$0.587483\pi$
$648$	893235.	0.0835657
$649$	−3.42617e6	−0.319299
$650$	1.16070e7	1.07755
$651$	2.44354e7	2.25979
$652$	1.53718e6	0.141614
$653$	−1.76847e7	−1.62298	−0.811492	−	0.584364i	$-0.801344\pi$
$653$	−1.76847e7	−1.62298	−0.811492	+	0.584364i	$0.801344\pi$
$654$	2.23096e7	2.03961
$655$	−30881.3	−0.00281250
$656$	9.61700e6	0.872529
$657$	−2.34909e7	−2.12318
$658$	1.74317e6	0.156955
$659$	1.07891e7	0.967769	0.483884	−	0.875132i	$-0.339226\pi$
$659$	1.07891e7	0.967769	0.483884	+	0.875132i	$0.339226\pi$
$660$	−2228.80	−0.000199164 0
$661$	−1.27678e7	−1.13662	−0.568308	−	0.822816i	$-0.692402\pi$
$661$	−1.27678e7	−1.13662	−0.568308	+	0.822816i	$0.692402\pi$
$662$	−8.77773e6	−0.778461
$663$	−1.27318e7	−1.12488
$664$	−5.72352e6	−0.503782
$665$	46380.5	0.00406707
$666$	−115770.	−0.0101137
$667$	−1.17724e7	−1.02459
$668$	2.02139e6	0.175270
$669$	−1.16215e7	−1.00392
$670$	−126577.	−0.0108935
$671$	922101.	0.0790628
$672$	4.46480e6	0.381399
$673$	5.05831e6	0.430495	0.215247	−	0.976560i	$-0.430944\pi$
$673$	5.05831e6	0.430495	0.215247	+	0.976560i	$0.430944\pi$
$674$	−1.25193e7	−1.06152
$675$	−1.10597e7	−0.934294
$676$	−308371.	−0.0259542
$677$	1.48127e7	1.24211	0.621057	−	0.783766i	$-0.286704\pi$
$677$	1.48127e7	1.24211	0.621057	+	0.783766i	$0.286704\pi$
$678$	−2.42635e7	−2.02712
$679$	2.00946e6	0.167265
$680$	63448.9	0.00526201
$681$	2.85217e7	2.35672
$682$	−2.07336e6	−0.170692
$683$	−9.52658e6	−0.781421	−0.390711	−	0.920514i	$-0.627771\pi$
$683$	−9.52658e6	−0.781421	−0.390711	+	0.920514i	$0.627771\pi$
$684$	695388.	0.0568312
$685$	−61005.2	−0.00496753
$686$	−5.28108e6	−0.428462
$687$	1.62479e7	1.31343
$688$	−1.70156e6	−0.137049
$689$	−2.07702e7	−1.66683
$690$	−80890.9	−0.00646810
$691$	−4.04497e6	−0.322270	−0.161135	−	0.986932i	$-0.551516\pi$
$691$	−4.04497e6	−0.322270	−0.161135	+	0.986932i	$0.551516\pi$
$692$	440860.	0.0349973
$693$	−4.20294e6	−0.332445
$694$	−1.32437e7	−1.04379
$695$	119743.	0.00940349
$696$	4.23278e7	3.31209
$697$	−7.70590e6	−0.600816
$698$	−2.35191e7	−1.82718
$699$	−1.47443e7	−1.14138
$700$	1.54374e6	0.119077
$701$	1.78401e6	0.137120	0.0685602	−	0.997647i	$-0.478159\pi$
$701$	1.78401e6	0.137120	0.0685602	+	0.997647i	$0.478159\pi$
$702$	−1.31469e7	−1.00688
$703$	34096.9	0.00260212
$704$	−2.31290e6	−0.175883
$705$	−22222.9	−0.00168394
$706$	4.84055e6	0.365496
$707$	1.78250e7	1.34116
$708$	−3.87646e6	−0.290638
$709$	−1.22322e7	−0.913878	−0.456939	−	0.889498i	$-0.651054\pi$
$709$	−1.22322e7	−0.913878	−0.456939	+	0.889498i	$0.651054\pi$
$710$	−27729.6	−0.00206442
$711$	3.69010e7	2.73756
$712$	1.22542e7	0.905913
$713$	7.68958e6	0.566473
$714$	1.65708e7	1.21646
$715$	−20677.1	−0.00151260
$716$	−305787.	−0.0222913
$717$	1.85124e7	1.34482
$718$	9.79938e6	0.709394
$719$	8.42924e6	0.608088	0.304044	−	0.952658i	$-0.401663\pi$
$719$	8.42924e6	0.608088	0.304044	+	0.952658i	$0.401663\pi$
$720$	161518.	0.0116115
$721$	−1.43554e7	−1.02844
$722$	−1.13376e7	−0.809428
$723$	−3.94128e7	−2.80409
$724$	−917691.	−0.0650654
$725$	2.80286e7	1.98041
$726$	−2.11525e7	−1.48943
$727$	1.10329e7	0.774201	0.387101	−	0.922037i	$-0.373477\pi$
$727$	1.10329e7	0.774201	0.387101	+	0.922037i	$0.373477\pi$
$728$	2.16280e7	1.51247
$729$	−2.33632e7	−1.62822
$730$	150414.	0.0104468
$731$	1.36342e6	0.0943708
$732$	1.04329e6	0.0719660
$733$	−5.02000e6	−0.345099	−0.172550	−	0.985001i	$-0.555201\pi$
$733$	−5.02000e6	−0.345099	−0.172550	+	0.985001i	$0.555201\pi$
$734$	−1.26496e7	−0.866633
$735$	−124920.	−0.00852933
$736$	1.40503e6	0.0956072
$737$	−3.37824e6	−0.229098
$738$	−2.16402e7	−1.46258
$739$	2.49061e6	0.167762	0.0838810	−	0.996476i	$-0.473268\pi$
$739$	2.49061e6	0.167762	0.0838810	+	0.996476i	$0.473268\pi$
$740$	−75.7506	−5.08518e−6 0
$741$	1.05304e7	0.704529
$742$	2.70330e7	1.80254
$743$	−1.21111e7	−0.804847	−0.402423	−	0.915454i	$-0.631832\pi$
$743$	−1.21111e7	−0.804847	−0.402423	+	0.915454i	$0.631832\pi$
$744$	−2.76480e7	−1.83118
$745$	−85590.9	−0.00564985
$746$	1.60506e7	1.05595
$747$	1.16746e7	0.765495
$748$	143680.	0.00938952
$749$	3.28294e7	2.13825
$750$	385195.	0.0250051
$751$	2.21669e7	1.43418	0.717092	−	0.696978i	$-0.245472\pi$
$751$	2.21669e7	1.43418	0.717092	+	0.696978i	$0.245472\pi$
$752$	−1.78790e6	−0.115292
$753$	1.14408e7	0.735310
$754$	3.33181e7	2.13428
$755$	60115.8	0.00383814
$756$	−1.74854e6	−0.111268
$757$	1.03112e7	0.653986	0.326993	−	0.945027i	$-0.393965\pi$
$757$	1.03112e7	0.653986	0.326993	+	0.945027i	$0.393965\pi$
$758$	9.57590e6	0.605350
$759$	−2.15891e6	−0.136029
$760$	−52478.2	−0.00329568
$761$	5.23003e6	0.327373	0.163686	−	0.986512i	$-0.447661\pi$
$761$	5.23003e6	0.327373	0.163686	+	0.986512i	$0.447661\pi$
$762$	−3.86761e7	−2.41299
$763$	2.75272e7	1.71179
$764$	−1.10740e6	−0.0686387
$765$	−129421.	−0.00799560
$766$	−1.12180e7	−0.690783
$767$	−3.59627e7	−2.20731
$768$	−7.24005e6	−0.442933
$769$	1.16812e7	0.712315	0.356157	−	0.934426i	$-0.384087\pi$
$769$	1.16812e7	0.712315	0.356157	+	0.934426i	$0.384087\pi$
$770$	26911.8	0.00163575
$771$	2.80847e7	1.70151
$772$	−254504.	−0.0153692
$773$	1.35127e7	0.813379	0.406690	−	0.913566i	$-0.366683\pi$
$773$	1.35127e7	0.813379	0.406690	+	0.913566i	$0.366683\pi$
$774$	3.82885e6	0.229729
$775$	−1.83079e7	−1.09493
$776$	−2.27365e6	−0.135540
$777$	−233167.	−0.0138553
$778$	−9.75702e6	−0.577920
$779$	6.37351e6	0.376301
$780$	−23394.6	−0.00137682
$781$	−740082.	−0.0434162
$782$	5.21465e6	0.304936
$783$	−3.17470e7	−1.85054
$784$	−1.00502e7	−0.583962
$785$	115210.	0.00667294
$786$	9.12553e6	0.526868
$787$	−2.08780e7	−1.20158	−0.600789	−	0.799407i	$-0.705147\pi$
$787$	−2.08780e7	−1.20158	−0.600789	+	0.799407i	$0.705147\pi$
$788$	528529.	0.0303217
$789$	4.39862e7	2.51550
$790$	−236280.	−0.0134698
$791$	−2.99381e7	−1.70131
$792$	4.75551e6	0.269392
$793$	9.67881e6	0.546562
$794$	1.00167e6	0.0563866
$795$	−344632.	−0.0193392
$796$	−459045.	−0.0256787
$797$	−1.17024e7	−0.652573	−0.326286	−	0.945271i	$-0.605797\pi$
$797$	−1.17024e7	−0.652573	−0.326286	+	0.945271i	$0.605797\pi$
$798$	−1.37056e7	−0.761887
$799$	1.43260e6	0.0793888
$800$	−3.34520e6	−0.184798
$801$	−2.49958e7	−1.37653
$802$	−1.84220e7	−1.01135
$803$	4.01444e6	0.219703
$804$	−3.82223e6	−0.208534
$805$	−99809.1	−0.00542851
$806$	−2.17630e7	−1.18000
$807$	3.07901e7	1.66428
$808$	−2.01685e7	−1.08679
$809$	−2.76467e7	−1.48516	−0.742578	−	0.669760i	$-0.766397\pi$
$809$	−2.76467e7	−1.48516	−0.742578	+	0.669760i	$0.766397\pi$
$810$	11666.4	0.000624774 0
$811$	−8.32113e6	−0.444253	−0.222126	−	0.975018i	$-0.571300\pi$
$811$	−8.32113e6	−0.444253	−0.222126	+	0.975018i	$0.571300\pi$
$812$	4.43132e6	0.235854
$813$	3.31375e7	1.75830
$814$	19784.4	0.00104655
$815$	236623.	0.0124785
$816$	−1.69960e7	−0.893554
$817$	−1.12768e6	−0.0591059
$818$	−2.30713e6	−0.120556
$819$	−4.41161e7	−2.29820
$820$	−14159.6	−0.000735385 0
$821$	8.01626e6	0.415063	0.207531	−	0.978228i	$-0.433457\pi$
$821$	8.01626e6	0.415063	0.207531	+	0.978228i	$0.433457\pi$
$822$	1.80273e7	0.930573
$823$	4.63830e6	0.238704	0.119352	−	0.992852i	$-0.461918\pi$
$823$	4.63830e6	0.238704	0.119352	+	0.992852i	$0.461918\pi$
$824$	1.62428e7	0.833378
$825$	5.14011e6	0.262928
$826$	4.68065e7	2.38702
$827$	5.55667e6	0.282521	0.141261	−	0.989972i	$-0.454884\pi$
$827$	5.55667e6	0.282521	0.141261	+	0.989972i	$0.454884\pi$
$828$	−1.49645e6	−0.0758554
$829$	2.47536e7	1.25098	0.625491	−	0.780231i	$-0.284899\pi$
$829$	2.47536e7	1.25098	0.625491	+	0.780231i	$0.284899\pi$
$830$	−74753.7	−0.00376650
$831$	4.93046e7	2.47676
$832$	−2.42773e7	−1.21588
$833$	8.05302e6	0.402111
$834$	−3.53846e7	−1.76156
$835$	311159.	0.0154442
$836$	−118837.	−0.00588080
$837$	2.07367e7	1.02312
$838$	2.06914e7	1.01784
$839$	−3.24512e7	−1.59157	−0.795785	−	0.605579i	$-0.792942\pi$
$839$	−3.24512e7	−1.59157	−0.795785	+	0.605579i	$0.792942\pi$
$840$	358865.	0.0175482
$841$	5.99451e7	2.92256
$842$	3.80347e7	1.84884
$843$	−2.80067e7	−1.35735
$844$	2.02392e6	0.0977994
$845$	−47468.6	−0.00228699
$846$	4.02313e6	0.193258
$847$	−2.60995e7	−1.25004
$848$	−2.77267e7	−1.32406
$849$	3.14899e7	1.49935
$850$	−1.24154e7	−0.589407
$851$	−73375.3	−0.00347317
$852$	−837349.	−0.0395191
$853$	2.47564e7	1.16497	0.582485	−	0.812841i	$-0.302080\pi$
$853$	2.47564e7	1.16497	0.582485	+	0.812841i	$0.302080\pi$
$854$	−1.25973e7	−0.591060
$855$	107043.	0.00500777
$856$	−3.71456e7	−1.73270
$857$	1.28652e7	0.598363	0.299182	−	0.954196i	$-0.403286\pi$
$857$	1.28652e7	0.598363	0.299182	+	0.954196i	$0.403286\pi$
$858$	6.11014e6	0.283356
$859$	1.98227e6	0.0916601	0.0458300	−	0.998949i	$-0.485407\pi$
$859$	1.98227e6	0.0916601	0.0458300	+	0.998949i	$0.485407\pi$
$860$	2505.28	0.000115508 0
$861$	−4.35844e7	−2.00366
$862$	−1.14130e7	−0.523157
$863$	−3.11840e6	−0.142529	−0.0712647	−	0.997457i	$-0.522704\pi$
$863$	−3.11840e6	−0.142529	−0.0712647	+	0.997457i	$0.522704\pi$
$864$	3.78898e6	0.172679
$865$	67863.0	0.00308384
$866$	−8.55964e6	−0.387847
$867$	−2.19435e7	−0.991421
$868$	−2.89449e6	−0.130399
$869$	−6.30613e6	−0.283279
$870$	552835.	0.0247627
$871$	−3.54596e7	−1.58376
$872$	−3.11462e7	−1.38712
$873$	4.63772e6	0.205953
$874$	−4.31301e6	−0.190986
$875$	475282.	0.0209861
$876$	4.54204e6	0.199982
$877$	−2.15790e7	−0.947398	−0.473699	−	0.880687i	$-0.657082\pi$
$877$	−2.15790e7	−0.947398	−0.473699	+	0.880687i	$0.657082\pi$
$878$	3.83267e7	1.67790
$879$	−6.52218e6	−0.284722
$880$	−27602.3	−0.00120154
$881$	−1.27720e7	−0.554393	−0.277196	−	0.960813i	$-0.589405\pi$
$881$	−1.27720e7	−0.554393	−0.277196	+	0.960813i	$0.589405\pi$
$882$	2.26150e7	0.978870
$883$	8.80113e6	0.379871	0.189936	−	0.981797i	$-0.439172\pi$
$883$	8.80113e6	0.379871	0.189936	+	0.981797i	$0.439172\pi$
$884$	1.50814e6	0.0649098
$885$	−596716.	−0.0256100
$886$	1.36012e7	0.582092
$887$	−3.47818e7	−1.48437	−0.742187	−	0.670192i	$-0.766212\pi$
$887$	−3.47818e7	−1.48437	−0.742187	+	0.670192i	$0.766212\pi$
$888$	263822.	0.0112274
$889$	−4.77214e7	−2.02516
$890$	160050.	0.00677301
$891$	311366.	0.0131394
$892$	1.37662e6	0.0579300
$893$	−1.18490e6	−0.0497225
$894$	2.52924e7	1.05839
$895$	−47070.8	−0.00196424
$896$	2.58932e7	1.07750
$897$	−2.26610e7	−0.940368
$898$	−2.54254e6	−0.105215
$899$	−5.25531e7	−2.16870
$900$	3.56286e6	0.146620
$901$	2.22168e7	0.911737
$902$	3.69816e6	0.151345
$903$	7.71150e6	0.314716
$904$	3.38741e7	1.37863
$905$	−141263.	−0.00573334
$906$	−1.77644e7	−0.719003
$907$	1.91865e7	0.774420	0.387210	−	0.921992i	$-0.373439\pi$
$907$	1.91865e7	0.774420	0.387210	+	0.921992i	$0.373439\pi$
$908$	−3.37853e6	−0.135992
$909$	4.11390e7	1.65137
$910$	282479.	0.0113079
$911$	834307.	0.0333066	0.0166533	−	0.999861i	$-0.494699\pi$
$911$	834307.	0.0333066	0.0166533	+	0.999861i	$0.494699\pi$
$912$	1.40573e7	0.559647
$913$	−1.99512e6	−0.0792121
$914$	−3.29242e7	−1.30362
$915$	160597.	0.00634139
$916$	−1.92464e6	−0.0757899
$917$	1.12598e7	0.442187
$918$	1.40625e7	0.550753
$919$	1.11037e7	0.433690	0.216845	−	0.976206i	$-0.430423\pi$
$919$	1.11037e7	0.433690	0.216845	+	0.976206i	$0.430423\pi$
$920$	112931.	0.00439890
$921$	−3.91080e7	−1.51921
$922$	4.02708e7	1.56014
$923$	−7.76826e6	−0.300137
$924$	812652.	0.0313130
$925$	174698.	0.00671324
$926$	−2.23602e7	−0.856935
$927$	−3.31315e7	−1.26631
$928$	−9.60242e6	−0.366025
$929$	−1.03857e7	−0.394816	−0.197408	−	0.980321i	$-0.563252\pi$
$929$	−1.03857e7	−0.394816	−0.197408	+	0.980321i	$0.563252\pi$
$930$	−361105.	−0.0136907
$931$	−6.66061e6	−0.251849
$932$	1.74653e6	0.0658622
$933$	1.64087e7	0.617120
$934$	−6.40063e6	−0.240080
$935$	22117.2	0.000827372 0
$936$	4.99161e7	1.86231
$937$	−2.10627e7	−0.783729	−0.391865	−	0.920023i	$-0.628170\pi$
$937$	−2.10627e7	−0.783729	−0.391865	+	0.920023i	$0.628170\pi$
$938$	4.61518e7	1.71270
$939$	−5.33209e6	−0.197348
$940$	2632.40	9.71701e−5 0
$941$	−3.67199e7	−1.35185	−0.675924	−	0.736971i	$-0.736255\pi$
$941$	−3.67199e7	−1.35185	−0.675924	+	0.736971i	$0.736255\pi$
$942$	−3.40451e7	−1.25005
$943$	−1.37156e7	−0.502267
$944$	−4.80076e7	−1.75339
$945$	−269159.	−0.00980457
$946$	−654325.	−0.0237720
$947$	1.07332e7	0.388914	0.194457	−	0.980911i	$-0.437706\pi$
$947$	1.07332e7	0.388914	0.194457	+	0.980911i	$0.437706\pi$
$948$	−7.13493e6	−0.257851
$949$	4.21375e7	1.51881
$950$	1.02687e7	0.369155
$951$	−9.66428e6	−0.346512
$952$	−2.31344e7	−0.827304
$953$	4.10240e7	1.46321	0.731603	−	0.681731i	$-0.238772\pi$
$953$	4.10240e7	1.46321	0.731603	+	0.681731i	$0.238772\pi$
$954$	6.23906e7	2.21946
$955$	−170465.	−0.00604821
$956$	−2.19287e6	−0.0776013
$957$	1.47547e7	0.520776
$958$	2.01575e7	0.709617
$959$	2.22434e7	0.781005
$960$	−402824.	−0.0141071
$961$	5.69795e6	0.199026
$962$	207666.	0.00723483
$963$	7.57683e7	2.63283
$964$	4.66862e6	0.161807
$965$	−39176.6	−0.00135428
$966$	2.94940e7	1.01693
$967$	2.93253e7	1.00850	0.504251	−	0.863557i	$-0.331769\pi$
$967$	2.93253e7	1.00850	0.504251	+	0.863557i	$0.331769\pi$
$968$	2.95309e7	1.01295
$969$	−1.12638e7	−0.385368
$970$	−29695.7	−0.00101336
$971$	3.44554e6	0.117276	0.0586381	−	0.998279i	$-0.481324\pi$
$971$	3.44554e6	0.117276	0.0586381	+	0.998279i	$0.481324\pi$
$972$	2.90394e6	0.0985877
$973$	−4.36601e7	−1.47843
$974$	3.86934e7	1.30689
$975$	5.39530e7	1.81763
$976$	1.29205e7	0.434165
$977$	3.77647e7	1.26576	0.632878	−	0.774252i	$-0.281874\pi$
$977$	3.77647e7	1.26576	0.632878	+	0.774252i	$0.281874\pi$
$978$	−6.99230e7	−2.33762
$979$	4.27162e6	0.142441
$980$	14797.4	0.000492175 0
$981$	6.35311e7	2.10772
$982$	−3.97352e7	−1.31491
$983$	1.69058e7	0.558024	0.279012	−	0.960288i	$-0.409993\pi$
$983$	1.69058e7	0.558024	0.279012	+	0.960288i	$0.409993\pi$
$984$	4.93145e7	1.62363
$985$	81358.2	0.00267184
$986$	−3.56387e7	−1.16743
$987$	8.10277e6	0.264753
$988$	−1.24737e6	−0.0406540
$989$	2.42673e6	0.0788915
$990$	62110.8	0.00201409
$991$	1.83818e7	0.594570	0.297285	−	0.954789i	$-0.403919\pi$
$991$	1.83818e7	0.594570	0.297285	+	0.954789i	$0.403919\pi$
$992$	6.27219e6	0.202367
$993$	−4.08016e7	−1.31312
$994$	1.01106e7	0.324572
$995$	−70662.3	−0.00226272
$996$	−2.25733e6	−0.0721019
$997$	−2.05937e7	−0.656139	−0.328069	−	0.944654i	$-0.606398\pi$
$997$	−2.05937e7	−0.656139	−0.328069	+	0.944654i	$0.606398\pi$
$998$	1.40679e7	0.447099
$999$	−197874.	−0.00627298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.7	✓	10
3.2	odd	2		387.6.a.e.1.4		10
4.3	odd	2		688.6.a.h.1.2		10
5.4	even	2		1075.6.a.b.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.7	✓	10	1.1	even	1	trivial
387.6.a.e.1.4		10	3.2	odd	2
688.6.a.h.1.2		10	4.3	odd	2
1075.6.a.b.1.4		10	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} +O(q^{10})\)	\(q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} -2.46078 q^{10} -65.6764 q^{11} -74.3080 q^{12} -689.371 q^{13} +897.236 q^{14} -11.4385 q^{15} -920.259 q^{16} +737.385 q^{17} +2070.77 q^{18} -609.887 q^{19} +1.35494 q^{20} +4170.63 q^{21} -353.880 q^{22} +1312.45 q^{23} -4718.95 q^{24} -3124.79 q^{25} -3714.50 q^{26} +3539.34 q^{27} -494.030 q^{28} -8969.74 q^{29} -61.6333 q^{30} +5858.93 q^{31} +1070.53 q^{32} -1644.94 q^{33} +3973.21 q^{34} -76.0477 q^{35} -1140.19 q^{36} -55.9069 q^{37} -3286.22 q^{38} -17266.1 q^{39} +86.0458 q^{40} -10450.3 q^{41} +22472.4 q^{42} +1849.00 q^{43} +194.851 q^{44} -175.514 q^{45} +7071.82 q^{46} +1942.82 q^{47} -23049.0 q^{48} +10921.1 q^{49} -16837.1 q^{50} +18468.7 q^{51} +2045.25 q^{52} +30129.2 q^{53} +19070.8 q^{54} +29.9941 q^{55} -31373.5 q^{56} -15275.3 q^{57} -48331.2 q^{58} +52167.4 q^{59} +33.9361 q^{60} -14040.1 q^{61} +31569.4 q^{62} +63994.7 q^{63} +35216.6 q^{64} +314.832 q^{65} -8863.36 q^{66} +51437.7 q^{67} -2187.70 q^{68} +32872.0 q^{69} -409.764 q^{70} +11268.6 q^{71} -72408.2 q^{72} -61124.5 q^{73} -301.240 q^{74} -78264.2 q^{75} +1809.44 q^{76} -10936.3 q^{77} -93034.1 q^{78} +96018.3 q^{79} +420.278 q^{80} -4740.91 q^{81} -56308.8 q^{82} +30378.0 q^{83} -12373.6 q^{84} -336.760 q^{85} +9962.86 q^{86} -224658. q^{87} +12374.1 q^{88} -65040.4 q^{89} -945.710 q^{90} -114792. q^{91} -3893.84 q^{92} +146744. q^{93} +10468.4 q^{94} +278.532 q^{95} +26812.8 q^{96} +12067.6 q^{97} +58845.3 q^{98} -25240.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * q^99

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